More than 200 members of Britain’s most distinguished families called on the Government to end the “outdated and manifestly unfair” laws of succession.

In a letter to The Daily Telegraph, they argue that the example of the Royal succession, where a first-born daughter of the Duke and Duchess of Cambridge could inherit the crown, should be followed by legislation for the nobility.

They called for an end to “gender discrimination” which means that daughters are excluded from inheriting their father’s title and estate.

However Number 10 sources on Monday that there were no plans to change the laws of succession among noble families.

A Cabinet Office spokesman said: “The Government has no plans to change the rule on hereditary peerages during this parliament.

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"As was made clear during the debates on the Succession to the Crown Act, there are differences between the rules regarding hereditary peerages and the rules governing succession to the Crown.

“Changes to the law on succession to the Crown can be effected without any change to the legitimate expectations of those in the line of succession. Changes to the rules governing succession to hereditary titles would be far more complicated to implement fairly.“

The anomaly was at the heart of ITV’s highly rated fictional serial Downton Abbey, in which Lady Mary, the eldest child of Robert Crawley, the fifth Earl of Grantham, was unable to inherit the family seat because it must pass to a male heir.

The demand was also backed by more than 20 MPs so far, including Dr Sarah Wollaston, Aidan Burley and Crispin Blunt.

The campaign was begun by the Countess of Clancarty, Lady Liza Campbell, the Hon Sarah Long and the Earl of Balfour, who called themselves “The Hares” after Lord Trefgarne told the House of Lords the Royal succession Bill had “set running the hare of what happens to the hereditary peerage”.